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A comment on List of unusual Wikipedia articles. Parent comment

Re:List of unusual Wikipedia articles by martincmartin on Saturday January 02, 2010 @05:10PM (#1027752)
Yes, and that's not a contradiction.

The problem comes with the set of all sets that don't contain themselves. Does that set contain itself? Both "yes" and "no" lead to contradiction. That contradiction is the basis of Godel's Incompleteness Theorem, the Halting Problem and others.

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Re:List of unusual Wikipedia articles by gambling8nt on Saturday January 02, 2010 @09:15PM (#1028069)
The collection of all sets is not a set under ZF set theory, regardless of choice.

Such a collection, if it were a set, would imply the existence of a set of all sets that did not contain themselves from the axiom schema of specification.

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